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arXiv · 1907.05946

Commutators of potential type operators with Lipschitz symbols on variable Lebesgue spaces with different weights

Luciana Melchiori·Gladis Pradolini·Wilfredo Ramos
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Abstract

We prove that a generalized Fefferman-Phong type condition on a pair of weights $u$ and $v$ is sufficient for the boundedness of the commutators of potential type operators from $L^{p(\cdot)}_v$ into $L^{q(\cdot)}_u$. We also give an improvement of this result in the sense that we not only consider a variable version of power bump conditions, but also weaker norms related to Musielak-Orlicz functions. We consider a wider class of symbols including Lipschitz symbols and some generalizations.

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Luciana Melchiori, Gladis Pradolini, Wilfredo Ramos. 2019-07-12. Commutators of potential type operators with Lipschitz symbols on variable Lebesgue spaces with different weights. https://arxiv.org/abs/1907.05946

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